Question

A vessel is filled with liquid, 3 parts
of which are water and 5 parts
syrup. How much of the mixture
must be drawn off and replaced
with water so that the mixture may
be half water and half syrup ?
a) 1/3 b) 1/4
c) 1/5 d) 1/7​

Answer 1

Answer:

(b)1/4

Step-by-step explanation:

let total quantity of mixture = 64g

water = 3/8 * 64 = 24g

syrup = 5/8 * 64 = 40g

mixture needs to be drawn of

= (40- 24)/64 =16/64 = 1/4 th part

option(b) is correct.

Answer 2

Suppose the vessel initially contains 8 liters of liquid.

Let x liters of this liquid be replaced with water.

Water in new mixture = (3-3x/8+x)

Syrup in new mixture = (5-5x/8)

Then (3-3x/8+x) = (5-5x/8)

5x + 24 = 40 - 5x

10x=16

==>x=8/5

So part of mixture replaced is 8/5*1/8=1/5